Related papers: Dynamical phase transition in the simplest molecul…
The first arrivals among $N$ Brownian particles is ubiquitous in the life sciences, as it often trigger cellular processes from the molecular level. We study here the case where stochastic particles, which represent molecules, proteins or…
Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…
We perform molecular dynamics simulation of a small number of particles in a box with periodic boundary conditions from a view point of chaotic dynamical systems. There is a transition at a critical energy E_c that each particle is confined…
We studied the step dynamics during crystal sublimation and growth in the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps. For this limit we formulate a model free of the quasi-static…
The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero…
We study the stability in finite times of the trajectories of interacting particles. Our aim is to show that in average and uniformly in the number of particles, two trajectories whose initial positions in phase space are close, remain…
We perform computer simulations of a Cahn-Hilliard model of phase separation which has dynamical asymmetry between the two coexisting phases. The dynamical asymmetry is incorporated by considering a mobility function which is order…
Classical phase transitions, like solid-liquid-gas or order-disorder spin magnetic phases, are all driven by thermal energy fluctuations by varying the temperature. On the other hand, quantum phase transitions happen at absolute zero…
A one-dimensional model on a line of the length L is investigated, which involves particle diffusion as well as single particle annihilation. There are also creation and annihilation at the boundaries. The static and dynamical behaviors of…
Quantum phase transitional behavior of a finite periodic XX spin-1/2 chain with nearest neighbor interaction in a uniform transverse field is studied based on the simple exact solutions. It is found that there are [N/2] level-crossing…
We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and…
A two species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behavior which…
Phase separation plays an role in determining the self-assembly of biological and soft-matter systems. In biological systems, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The…
We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of…
We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves…
This article studies the dynamics of a finite chain with infinite components. The equation which permits us to find the probability distribution of the chain length is constructed and analysed. This research is a continuation of paper…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
A stochastic differential equation that describes the dynamics of single-domain magnetic particles at any temperature is derived using a classical formalism. The deterministic terms recover existing theory and the stochastic process takes…
The origin of the non commutativity of the limits $t \to \infty$ and $N \to \infty$ in the dynamics of first order transitions is investigated. In the large-N model, i.e. $N \to \infty$ taken first, the low temperature phase is…
Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are…